Electronic Structures and Spectral Properties of Endohedral Fullerenes

Coordination Chemistry Reviews 249 (2005) 1111–1132

Review Electronic structures and spectral properties of endohedral fullerenes

Suchi Guhaa,∗, Kazuo Nakamotob

a Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA b Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, WI 53217, USA Received 29 September 2004; accepted 8 November 2004 Available online 5 January 2005 Contents

1. Introduction ...... 1112 2. Theoretical background...... 1112 2.1. A simple model for the electronic structure of C60 ...... 1112 2.2. Quantum chemical methods...... 1113 2.3. Ab initio calculations of endohedral fullerenes ...... 1114 2.4. Vibrational spectra ...... 1115 2.4.1. Raman intensity calculations ...... 1115 2.4.2. IR absorption intensity calculations ...... 1116 3. C60 and C70 ...... 1116 3.1. Electronic states of alkali-doped exohedral C60 ...... 1117 3.2. Endohedral C60 and C70 ...... 1118 3.2.1. Kr@C60 ...... 1118 3.2.2. Li@C60 ...... 1119 3.2.3. M@C60 (M: rare-earth metal) ...... 1120 4. C72 and C74 ...... 1121 4.1. Ca@C72 and Ca@C74 ...... 1121 4.2. Eu@C74 ...... 1122 5. C78 ...... 1122 6. C80 ...... 1123 6.1. La2@C80 ...... 1123 6.2. Sc3N@C80 ...... 1124 7. C82 ...... 1126 8. C84 ...... 1128 9. Summary and prospect ...... 1130 Acknowledgements...... 1130 References...... 1130

Abstract

Endohedral fullerenes belong to a new class of compounds which are technologically and scientiﬁcally important owing to their unique structures and optoelectronic properties. This review focuses on theoretical calculations and spectroscopic (electronic, vibrational, and nuclear magnetic resonance (NMR)) studies of endohedral fullerenes thus far published. A theoretical background, with various computational

∗ Corresponding author. Tel.: +1 573 8843687; fax: +1 573 8824195. E-mail address: [email protected] (S. Guha).

0010-8545/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ccr.2004.11.017 1112 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 methods used for determining energy-optimized electronic structure and calculation of vibrational spectra, is presented. Further, theoretical and spectroscopic investigations of individual endohedral fullerenes are discussed. Such studies provide structural information about the carbon cage, position of the encapsulated species, and the degree of charge transfer. In particular, 13C NMR spectroscopy is indispensable for the determination of the cage symmetry. In some cases, NMR signals from 45Sc encapsulated species yield information about dynamic behavior inside the cage. Vis–NIR absorption spectra determine the HOMO–LUMO band-gap energy. IR and Raman spectroscopy play an important role in elucidating the nature of interaction between the cage and encapsulated species. Novel vibrations resulting from these interactions appear in the low-frequency region, and the corresponding force constants serve as a measure of the strength of their interaction. © 2004 Elsevier B.V. All rights reserved.

Keywords: Endohedral fullerenes; Density functional theory; UV–vis–NIR spectra; IR spectra; Raman spectra; C60;C70;C72;C74;C78;C80;C82;C84

1. Introduction have revealed the structure of the fullerene cages, the electronic states of metal atoms and fullerene cages, and how It was first proposed in 1985 that fullerenes could confine the electronic properties and chemical reactivities of empty atoms in their interior because of their closed-cage structure fullerene cages change upon endohedral metal doping. Re- [1]. Since then metal-containing endohedral fullerenes have cently, these investigations have been extended to endohe- attracted special attention as a new class of technologically dral fullerenes containing small molecules, such as Sc3N and relevant materials due to their combined fullerene-like and Y2C2. In this section we give a brief overview of some of the metallic properties. In most endohedral metallofullerenes, theoretical techniques of modern quantum chemistry that are introduction of metal atoms into carbon cages leads to an used for the electronic and vibrational structure calculations increase in the electron affinity relative to the corresponding of fullerenes and endohedral fullerenes. empty-cages [2,3]. Endohedral metallofullerenes hold great promise for applications in optoelectronic devices since vary- 2.1. A simple model for the electronic structure of C60 ing the encapsulated metal cluster can alter the optical and electronic properties, without changing the structural features For a perfectly spherical molecule, one can use spherical of the outer carbon shell. Enhancement of third-order non- harmonics to predict the electronic energy levels. A model linear optical susceptibility observed in endohedral metallo- for the electronic structure of C60 based on elementary quan- fullerenes further establishes them as potential candidates for tum mechanics and group theory can be found in Ref. [10]. nonlinear optical devices [4]. The spherical nature of a C60 molecule allows the electronic A variety of endohedral metallofullerenes have been re- states to be labeled by spherical harmonics [11]. In this sim- ported, but their investigations have been severely limited plest model the 60 ␲ electrons of C60 are described by spher- because they are typically formed in extremely low yields ical harmonic wavefunctions modified slightly by the icosa- (<0.5%). This article is intended to review the structural and hedral symmetry. To accommodate 60 electrons according spectroscopic investigations of the limited number of endohe- to the Pauli exclusion principle and Hund’s rule, the energy dral fullerenes thus far published [5–7] and for which UV–vis states corresponding to =0 to = 4 are completely filled. and vibrational data are available. These studies have shed The highest energy level corresponding to = 5 has 10 un- light on the effect of encapsulation on the carbon cage, the paired electrons. Since pristine C60 is an insulator and has no location of the encapsulated species inside the cage, and the unpaired electrons, the above scheme needs to be modified. nature of interaction between the carbon cage and the encap- One has to invoke the icosahedral symmetry which is a lower sulated species. This review is organized as follows: Section symmetry compared to a perfect sphere. The carbon-derived 2 gives a theoretical background on electronic structure cal- potential splits the degenerate energy levels above = 2 of the culation of fullerenes and empirical models for Raman and spherical potential. The = 5 shell with 11 degenerate states infrared absorption intensity calculations. In Sections 3–8 we splits into a five-fold degenerate highest occupied molecular discuss the following fullerene cages: C60 and C70,C72 and orbital (HOMO), a threefold degenerate lowest unoccupied C74,C78,C80,C82, and C84. In each of these sections, we molecular orbital (LUMO) and an additional threefold de- first discuss the structure of empty fullerene cages followed generate level at a higher energy, as shown in Fig. 1. Fifty ␲ by a discussion of their endohedral counterpart in terms of electrons fill orbitals from = 0 to 4 and 10 electrons occupy the electronic states, electronic and vibrational spectra, and part of the = 5 shell. nuclear magnetic resonance (NMR) spectra [5,7–9].

2. Theoretical background

Various theoretical techniques have been employed to study the electronic and structural (including vibrational) Fig. 1. The splitting of the = 5 energy level under icosahedral symmetry. properties of fullerenes and their derivatives. These studies Adapted from Ref. [10]. S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1113

The above model although quite simple correctly pre- tances. In the ab initio Hartree approximation the many elec- dicts the insulating behavior of C60 and the fact that the tron wavefunction is written as a product of the single particle HOMO–LUMO transition (hu → t1u) is optically forbidden. wavefunctions. Constraining the occupation numbers of the For an accurate description of the energy levels one must natural spinorbitals to either 0 or 1 leads to the Hartree–Fock rely on more sophisticated molecular orbital or band theory (HF) approximation. calculations. A detailed theoretical approach for electronic The choice of a basis set is an important starting point structure calculations of fullerenes and their derivatives can for most molecular quantum mechanical methods. For di- be found in the work by Cioslowski [12]. atomic molecules, the basis functions are usually taken as atomic orbitals (AO). Each AO can be represented as a lin- 2.2. Quantum chemical methods ear combination of one or more Slater-type orbitals (STO). For polyatomic molecules the above method is very time Molecular quantum mechanical methods are classified as consuming; other methods, such as nuclei centered Carte- ab initio or semi-empirical. In semi-empirical methods a sim- sian Gaussian-type functions are used for large fullerene-type pler Hamiltonian is used, compared to the actual molecular molecules [12]. The accuracy of computed wavefunctions Hamiltonian, and typically uses parameters whose values are improves with increasing number of basis functions. The ba- adjusted to fit experimental data. In contrast, an ab initio cal- sis sets fall into different categories such as, minimal (STO- culation uses the exact Hamiltonian. For a comprehensive 3G, SZ), split valence (4-31G and 6-31G), double-zeta (DZ), * * review of the various ab initio and semi-empirical methods triple-zeta (TZ), polarized (6-31G , 6-311G ), and diffuse ** used in quantum chemistry, see Ref. [13]. (6-311++G ). For a comprehensive review that explains the Within non-relativistic quantum mechanics, the station- above terminology and which basis set should be used for a ary wavefunctions of a chemical system composed of N elec- specific electronic calculation, see Ref. [15]. The above basis trons are the solutions of the time-independent Schrodinger¨ functions are available in the widely used ab initio program equation. One normally invokes the Born–Oppenheimer ap- GAUSSIAN 03 [16]. proximation where the nuclei interact through an effective The HF approximation ignores the correlation hole that potential [14]. The total wavefunction Ψ(ri, ui) can be ap- each electron dresses itself with and hence overestimates proximately written as a product of the many-electron states, the Coulomb repulsion between the electrons. Several ap- Ψe(r, u) and the nuclear wavefunction, ΨN(u). The electronic proximate electron correlation methods have been proposed. states depend parametrically on the displacement of the nu- Among these the Møller–Plesset second-order perturbation clei, represented collectively by u, and on the electronic co- theory (MP2) is a feasible large-scale ab initio calculation ordinates r. The electronic wavefunction can then be solved of the ground state properties. Semi-empirical approaches using of quantum chemistry have also played a vital role in the electronic structure calculations of organic molecules. See Hˆ e(r, u)Ψe(r, u) = EeΨe(r, u), (1) Chapter 2 of Ref. [12] for details on various ab initio and semi-empirical methods of electronic structure calculations Hˆ = T + V + V where e e ee eN; Te is the operator for the ki- and their application to fullerenes. netic energy of electrons, Vee is the potential energy of In recent years, density-functional theory (DFT), first pro- the repulsion between the electrons, VeN is the poten- pounded by Kohn and Sham [17], has become very popular tial energy of attraction between the electrons and the in quantum chemistry for electronic structure calculations nuclei. Full specification of the electronic wavefunction, of larger molecules. The main difference between DFT and Ψ r ,...,r , u ,...,u e( 1 N 1 N) requires inclusion of the elec- other ab initio methods is that in DFT one does not need the tronic spin. actual wavefunction; all that is required is the particle den- For a system of N electrons there are 3N spatial and N spin sity, which explains all the observables. For a simple intro- {r } coordinates. The spatial coordinates i are often combined duction to DFT, see Ref. [18]. The Hohenberg–Kohn theorem {x } Ψ with their spin to yield a set of i . e satisfies proper bound- states that the electronic structure of a system of interacting ∞ ary conditions (vanishes at ) and the asymmetry property electrons in the ground state in an external potential can be of the Pauli principle. In actual electronic structure calcula- completely determined by the electronic charge density ρ(r) tions, it is often more convenient to work with the one-particle [19]. The exact ground state energy functional can be written reduced density matrix: as: Γ x , x = n ψ∗ x ψ x , ( 1 1) i i ( 1) i( 1) (2) i EG[ρ] = T [ρ] + ρ(r)VN(r)dr which involves the one particle functions {ψi} called natu- 1 + ρ(r)V (r)dr + E [ρ], (3) ral spinorbitals [12]. The spinorbitals form an orthonormal 2 H XC set of functions and the corresponding occupation numbers {ni} sum up to N. The electron density ρ(r) has maxima at where T[ρ] is the kinetic energy of interacting electrons, the nuclear positions and decays exponentially at large dis- VN(r) is the electrostatic potential due to the nuclei, and 1114 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

VH(r), the Hartree potential, is the electrostatic potential due Table 1 Calculated ionization potentials (IP) and electron affinities (EA) in eV for to the electronic charge density ρ(r). EXC[ρ] is the so-called M@C and pristine fullerenes exchange-correlation. 82 Many DFT calculations are performed in the local density IP (eV) EA (eV) approximation (LDA) [20,21], where the charge density is Sc@C82 6.45 3.08 Y@C 6.22 3.20 measured for a small volume element; EXC assigned to this 82 La@C 6.19 3.22 region is then approximated as the exchange-correlation en- 82 Ce@C82 6.46 3.19 ergy of a volume element of a uniform electron gas of the Eu@C82 6.49 3.22 same density as the initial volume element that was picked. Gd@C82 6.25 3.20 This is an approximation since it ignores the fact that the C60 7.78 2.57 charge density in the solid varies from one volume element C70 7.64 2.69 Adapted from Ref. [7]. to the next. In LDA, EXC(ρ) is given by an integral of a function, which is well known from quantum Monte Carlo calculations [22] and depends only on the local value of ρ(r). rem is that the spinorbitals of the parent system do not change Bond dissociation energies obtained with the LDA method upon adding or removing an electron. One can also calculate are much more accurate than those offered by Hartree–Fock the IPs and the EAs by separately carrying out HF calcula- calculations [23]. However, LDA is known to overestimate tions for the parent system and the corresponding ions. The bond dissociation energies. This overbinding is reduced by differences between the respective IPs and the EAs yield the the use of gradient-corrected functionals [24] in place of the orbital relaxation energies. Table 1 gives the calculated IPs local-density functionals. The gradient-corrected functionals and the EAs (in eV) for M@C82 and pristine fullerenes, where depend not only on the electron density but also on its gradient M represents a metal atom [7]. The IP values for M@C82 are EB ρ [25]. The Becke functional [26], x [ ], for the exchange en- smaller, whereas the EA values of M@C82 are larger, than ergy of a closed-shell system and the Lee–Yang–Parr (LYP) those for pristine C60 and C70. This indicates that endohedral ELYP ρ functional [27], corr [ ], for the correlation energy have been metallofullerenes can act as a strong electron donor as well widely used. Although the exact correlation functional of the as an electron acceptor. Kohn–Sham theory is different from describing the correla- In endohedral metallofullerenes complexes, mixing be- tion energy in terms of the HF electron density, the same ap- tween atomic orbitals of the guest and molecular orbitals of proximate functionals are often employed in both approaches. the fullerene host cage is negligible. Binding in these com- In the hybrid approach, the electron density is calculated with plexes is dominated by electrostatic and polarization effects an ordinary self-consistent procedure, and the computed HF [30]. However, in endohedral compounds such as charge- energy is combined with the approximate electron correla- transfer complexes of C60,C70 and other higher fullerenes, tion energy. Accurate atomization energies, ionization po- substantial orbital mixing may be present resulting in a direct tentials, and electron affinities are obtained within the hybrid chemical bonding [31]. See Ref. [12] for a detailed theoret- approach, using the B3LYP functional, which depends on the ical analysis on bonding and charge transfer in endohedral one-particle density matrix rather than on the electron den- compounds and complexes. sity itself, since it depends on the exact HF exchange energy Among various endohedral species, C28 is the smallest EHF ρ x [ ], and is given by fullerene cage that successfully traps metal atoms inside the cage. HF-level calculations using a DZ basis set show that EB3LYP Γ = ELYP ρ + EB ρ − EHF ρ . corr ( ) corr [ ] x [ ] x [ ] (4) the binding energy of M@C28 (M: Mg, Al, etc.) is a good indicator of whether the C28 cage can trap metal atoms [32]. Electronic structure calculations based on DFT including These calculations show that elements with electronegativi- electron correlation effects utilize only a fraction of com- ties smaller than 1.54 eV are successfully trapped inside the putational time in comparison with wavefunction-based ap- C28 cage. Also, the smallest endohedral fullerene that can be proaches of quantum chemistry. Both the Kohn–Sham and formed for a given element is a function of its ionic radius. the hybrid formalisms have been implemented in a number See Table III of Ref. [32] for further details. of commercially available software packages, such as GAUS- To understand the motion of the encapsulated metals in- SIAN 03 [16] and Amsterdam density functional (ADF) [28], side the fullerene cage, Nagase et al. [7] have investigated the which are widely used for electronic structure calculations of electrostatic potential inside C80,C82, and C84 cages using fullerenes and endohedral fullerenes. HF calculations. Their finding is that the electrostatic potentials are all positive inside the cages, reflecting that the proba- 2.3. Ab initio calculations of endohedral fullerenes bility of finding electrons inside is much smaller than finding them outside. The situation changes drastically as electrons The negative orbital energies of the occupied and virtual are transferred onto carbon cages. Electrostatic potentials cal- 2− 4− spinorbitals give the ionization potential (IP) and the electron culated for C82 and C84 provide highly negative values affinities (EA), respectively, which is a direct consequence of implying that they are suitable for the accommodation of Koopmans’ theorem [29]. The philosophy behind this theo- cationic species. The encapsulated metals, therefore, do not S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1115 preserve a neutral state but prefer a highly cationic state. 2.4.1. Raman intensity calculations The positively charged metal ions are highly stabilized at the A complete theoretical analysis of the Raman spectrum minima of the electrostatic potentials. Hence, the electrostatic of fullerenes requires an accurate prediction of the Raman potentials play a dominant role in stabilizing endohedral met- intensities. Both the Raman frequencies and intensities are allofullerenes. In Sections 3–8, we will discuss the electronic sensitive to external perturbations such as, charge transfer, structure of the various endohedral fullerenes in details. crystal field and the isotope effect [33]. Raman intensities of C60 have been calculated using ab initio methods [38], semi-empirical quantum chemical models [44], and empir- 2.4. Vibrational spectra ical model, such as the bond polarizability model [45].In this section we will limit our discussion to the prediction of Several reviews have appeared on the vibrational structure Raman intensities using the bond polarizability model [46]. of fullerenes and nanotubes [33,34]. An extensive review on For a system of N atoms interacting via harmonic forces, the Raman and infrared spectroscopy of C60 by Menendez´ the normal mode frequencies {ωf} and amplitudes χ(f)of and Page [35] gives a detailed description of the various mode f, where f =1, ...,3N labels the normal modes, are normal mode calculations of C60 so far published. In the determined by a 3N × 3N matrix eigenvalue equation: last decade there has been a rapid development in the first- − ω2 χ f = , principles calculations of the vibrational spectra of C60, some ( f M) ( ) 0 (5) of which are mentioned below. where is the harmonic force constant matrix and M is First-principles normal mode calculations of fullerenes the mass matrix. Both the force constant and mass matrices based on DFT within the LDA approach give the best agree- are symmetric. The mode eigenvectors χ(f) are subjected to ment with the known C60 vibrational frequencies, with an the orthonormality condition χα(l|f )χα(l|f )ml = δff , average deviation ranging from 1.8% to 3.9%. The first prin- lα where m is the mass of atom l and the sum is over all sites ciples approach of Quong et al. [36] and Wang et al. [37] us- l and directions. In the harmonic approximation, the intensity ing different all-electron localized basis sets within the LDA of off-resonance first-order Stokes scattering is given by yield vibrational frequencies with deviations from the experimental values by 1.9% and 2.2%, respectively. Density 2 3N ( n(wf )+1) functional perturbation theory was used by Giannozzi and I −ω = Cω ω3 η η P ηη ( ) L S α β αβ,f Baroni [38] to compute the vibrational frequencies of C60, ωf f =1 αβ with an average deviation from experiment of only 1.8%. The calculations by Adams et al. [39] uses the LDA and the × δ(ω − ωf ), (6) Harris-energy-functional approximations [40], and expands ω and ω are the incident and scattered light frequencies; the many-electron wavefunction as a sum of one ‘s’ and three L S ω ≡ ω −ω is the Raman shift; η and η are unit vectors along ‘p’ pseudoatomic local orbitals per atom. With subsequent re- L S the incident and scattered polarization direction, respectively; finement they obtained a deviation from experiment by 3.9%. −1 n(ωf)≡[exp(βhω¯ f) − 1] is the thermal average occupa- A major advantage of their method is that it is computation- − tion number of mode f at temperature T =(k β) 1. Pαβ is ally very efficient. B ,f the derivative of the electronic polarizability tensor (where α Since the early 1990s when experimental vibrational fre- and β are Cartesian coordinates) with respect to the normal quencies (Raman and IR) became available, several empir- coordinate of mode f. ical methods were introduced and the force constants were The main assumption in the bond polarizability model calculated from fits to the Raman-active and infrared-active is that the electronic polarizability of a molecule is equal modes. Jishi et al. [41] used an eight-parameter model fit and to the sum of the electronic polarizabilities of the bonds Feldman et al. [42] used a seven-parameter model fit to the between nearest pair of atoms. The overall polarizability Raman-active and infrared-active modes. The adiabatic bond P = N πj charge model, which is among the best empirical models for αβ j=1 αβ is expressed as the summation of the in- a description of the lattice dynamics of tetrahedral semicon- dividual bond polarizabilities (π s) for the jth bond. One can ductors and graphite, has also been applied to fullerenes [43]. show that the bond polarizability for a given pair of atoms In contrast to pristine fullerenes, there are only a few can be written as the sum of an isotropic and an anisotropic theoretical studies on the vibrational spectra of endohedral tensor [47] fullerenes. Inclusion of a metal cluster such as Sc3N inside R R 1 α β 1 the fullerene cage may cause a significant amount of interac- παβ (R) = (α|| + 2α⊥)δαβ + (α|| − α⊥) − δαβ . 3 R2 3 tion between the cage and the metal cluster, and make such (7) calculations more complex. The vibrational spectra are suf- ficiently sensitive to distinguish the various cage isomers. The principal assumption here is that bond polarizabilities are However, comparison with experiments is not quite satisfac- functions of the bond lengths “R” only, i.e. α|| = α||(R) and tory since the fullerene cage may have several isomeric forms α⊥ = α⊥(R), where α|| is along the bond direction and α⊥ which give similar frequencies. is along the principal axes perpendicular to the bond. This 1116 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 approximation neglects the dependence of a bond’s polariz- have a higher formation energy than fullerenes with iso- ability on the motion of atoms not connected to that bond. lated pentagons, whereby a pentagon is completely sur- One can then show that rounded by hexagons. Since all the carbon atoms in C60 are equivalent, its 13C NMR spectrum exhibits a single ∂παβ [R(lB)] Pαβ,f =− χγ (l|f ), (8) signal at 143.23 ppm. The 174 (3 × 60 − 6) normal vi- ∂Rγ (lB) B lγ 0 brations of the C60 cage are classified into 2Ag +Au + 3F1g +4F1u +4F2g +5F2u +6Gg +6Gu +8Hg +7Hu under Ih where the sum on B for a fixed site l runs over all bonds that are symmetry [49]. However, only four F1u vibrations are IR- attached to the site. The above expression can be expressed active and two A and eight H vibrations are Raman-active α α g g as a sum of three contributions in terms of ||, ⊥ and their due to its high symmetry. As a result, four IR bands are ob- derivatives. See Ref. [47] for details. Using the mode eigen- −1 −1 −1 served at 527 cm (F1u(1)), 577 cm (F1u(2)), 1183 cm vectors obtained from first-principles calculations, together −1 (F1u(3)) and 1428 cm (F1u(4)), and ten Raman bands are with the polarizability parameters, Pαβ can be calculated, −1 −1 −1 ,f observed at 273 cm (Hg(1)), 437 cm (Hg(2)), 496 cm which when substituted in Eq. (6) results in the first-order −1 −1 −1 (Ag(1)), 710 cm (Hg(3)), 774 cm (Hg(4)), 1099 cm Raman intensity. −1 −1 −1 (Hg(5)), 1250 cm (Hg(6)), 1428 cm (Hg(7)), 1470 cm −1 (Ag(2)) and 1575 cm (Hg(8)) [50]. In general, vibrations 2.4.2. IR absorption intensity calculations above 1000 cm−1 are predominantly due to displacements For a sample containing N molecules per unit volume, the tangential to the C60 cage surface, whereas those below first-order contribution to the absorption is given by [35] 800 cm−1 are predominantly due to radial displacements. The two polarized (A ) Raman bands at 496 and 1470 cm−1 π2N g A ω = 2 |µ |2δ ω − ω , are assigned to the totally symmetric radial “breathing” and ( ) cn f ( f ) (9) 3 f “tangential stretching” (or pentagonal pinching) modes, respectively, while the lowest frequency band (depolarized) at where n is the medium’s refractive index, c is the speed of light 273 cm−1 is described as the “cage-squashing” mode (vide in vacuum, and µ f is the derivative of the dipole moment. infra). Therefore, the integrated absorption strength of a mode f is A standard technique in molecular spectroscopy is the in- proportional to |µf |2, which is related to the mode’s effective vestigation of isotope-induced shifts in the frequencies of vi- charge. brational modes. Since the natural abundance of 13C is 1.11%, In the literature there are several first-principles models 49% of all C60 molecules made from natural graphite con- 13 that compute the IR strengths in C60 and C70. Table 6 of Ref. tain one or more C isotopes. High resolution Raman spec- [35] gives the calculated relative absorption strengths of the tra of C60 molecules show that the pentagonal pinch mode at −1 first-order IR active modes in C60, using semi-empirical and 1470 cm has a fine structure due to the isotopic shifts. Fig. 2 first-principles (LDA) models. These theoretical IR strengths shows a high-resolution Raman spectrum of the 1470 cm−1 show a wide variation from model to model. Theoretical prediction of first-order IR strengths in C60 is more chal- lenging since they depend quite sensitively on the electronic states; derivatives of the mode dipole moment (µ f ) describe the vibrationally induced electronic charge redistribution and are more difficult to predict. It turns out that several phenomenological models, such as the classical model for effective charges developed by Fabian [48] predict the IR strengths in C60 quite accurately. This model depends only on the geometry of the vibrating molecule where the dipole moment of a give mode is described by the motion of 60 ␲ electrons. For a review of the several first-principles and phenomenological models that have been used for computing the IR strengths in pristine fullerenes, see Ref. [35].

3. C60 and C70

Fig. 2. Unpolarized Raman spectrum of a frozen solution of C60 in CS2 at The C60 cage consists of 20 hexagonal and 12 pen- 30 K. The solid line is a 3-Lorentzian fit to the experimental data. The highest tagonal faces with 60 carbon atoms being located at the frequency is assigned to the totally symmetric pentagonal-pinch Ag mode 12 vertices of a regular truncated icosahedron of I symme- in C60. The other two lines are assigned to the pentagonal-pinch mode h in molecules containing one and two 13C isotopes, respectively. The inset try. A C60 molecule follows the isolated pentagon rule shows the evolution of these peaks as the solution is heated. Reproduced (IPR), which states that fullerenes with adjacent pentagons from Ref. [51] with permission. S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1117 mode [51]. Three peaks are resolved, which show a striking correlation with the mass spectrum of C60 [52]. The highest −1 energy Raman peak at 1471 cm is the Ag mode of isotopi- 12 −1 cally pure C60 (60 C atoms). The second peak at 1470 cm 13 is from C60 molecules with one C isotope, and the third −1 peak at 1469 cm is assigned to C60 molecules with two 13C isotopes. The C70 molecule can be described as two hemispheri- cal caps of C60 molecules joined together by a belt of 10 carbon atoms [53]. There are eight different bond lengths in C70 ranging from 1.40 to 1.45 A.˚ It has a point group symmetry of D5h. The lower symmetry of C70 in comparison to C60 results in many more Raman-active and infrared-active modes. Group theoretical analysis indicates that C70 has 53 Raman-active modes and 31 infrared-active modes. The Raman-active modes correspond to the symme- + + try types 12A1 19E1 22E2 and the infrared-active modes + to 10A2 21E1. The Raman scattering intensities in molecular C60 and C70 are found to be well reproduced by a bond polarizability model with parameters similar to those obtained from hydro- carbons. The hydrocarbon polarizability parameters give a qualitative agreement with the experimental Raman spectra of C60 and C70. A marked improvement for C60 was found for a bond polarizability fit to the experimental Raman spectra obtained using off-resonance near infrared excitation [54]. Fig. 3. Experimental and predicted normalized Raman spectra of C60. The −1 Fig. 3 (thin solid line) shows the Raman intensities of C60 intensity of the Ag(2) line at 1470 cm has been set equal to unity, and obtained using first-principles vibrational eigenvectors along the calculated lines have been shifted from the experimental frequency, for clarity. The thick solid line represent the experimental data of Chase et al. with the fit polarizability parameters [47] within the bond po- [54], and the thin solid lines show the fit obtained from fitted polarizability larizability model. Recent work by Ren et al. [55] have fur- parameters. Reproduced from Ref. [47] with permission. ther improved the set of polarizability parameters for C60.It has been further shown that the polarizability parameters ob- M3C60, where M refers to an alkali metal; (b) the insulating tained for C60 can be transferred to higher fullerenes, such as M6C60 phase which adopts a body-centered structure (bcc); C70 and C60 polymers [56] to predict the Raman spectra. The and (c) an intermediate composition M4C60 of orthorhombic important consequence of this is that since the polarizabilities structure which is also insulating [58]. Spectroscopic studies are independent of the chemical environment they are trans- on these compounds provide information about the pertur- ferable between different compounds. As a result one can bation of the C60 structure resulting from metal to C60 cage predict the Raman intensities of new fullerene systems. So charge-transfer and the strength of the metal–C60 cage inter- far, to our knowledge there has been no published work on ex- action. A wide variety of experimental techniques like optical tending the bond polarizability model for predicting Raman absorption, [59] electron energy-loss spectroscopy [60] and intensities in charge-transfer or endohedral fullerene cages. nuclear magnetic resonance [61] have been used to probe the The degree of electronic coupling to the ␲ electron sys- electronic states of the fullerenes. tem of the fullerene depends on the nature of the endohedral The bonding character of an isolated C60 molecule is pre- atoms. The charge transfer process in metallic endohedral dominantly sp2 with a small admixture of sp3 character due to fullerenes is more complex than in exohedral alkali metal- nonzero curvature. The electronic states can be decomposed doped fullerenes. In the next section we first discuss the elec- into “␲”-like and “␴”-like states. The curvature of the surface tronic states of exohedral metal-doped C60 followed by the at a carbon atom induces a change in hybridization as com- electronic structures of endohedral C60 and C70. pared to graphite. As a result the ␲-like orbital is no longer purely pz orbital in character and the ␴-like orbital contains 3.1. Electronic states of alkali-doped exohedral C60 an admixture of pz. Thus the fullerenes are of intermediate hybridization. The interest in electronic properties of fullerenes dramat- Fig. 4 shows a schematic of the near-gap energy lev- 3− ically increased after the discovery of superconductivity at els of an isolated C60, and anions of the molecule, C60 6− 18 K in potassium doped C60 [57]. By intercalating C60 with and C60 , predicted by theoretical models [62,63]. It also alkali metals, a variety of new compounds have been formed. shows the number of electrons in each level. The HOMO There are three distinct bulk phases: (a) the superconducting level is the hu state and is fully occupied by 10 electrons. 1118 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

3− 6− Fig. 4. Schematic near gap energy levels of C60,C60 and C60 . The arrows in each level indicate electronic spins and the numbers in parenthesis denote the degeneracy of each level.

The HOMO–LUMO energy gap (between the hu state and the t1u state) is 1.9 eV. The lowest optically allowed transition between the valence band and the conduction band is from the hu state to the t1u +1(t1g) state in a C60 molecule. 3− For the C60 anions the picture is slightly different. In C60 the LUMO is half filled i.e., it has three electrons and the transition between this state and the next higher state, the t1g 3− state, is optically allowed. As a result C60 is a conductor, Fig. 5. The infrared spectra of C60 (top panel) and Kr@C60 (bottom panel). as opposed to C60, which is an insulator. This is observed in Adapted from Ref. [67]. the M3C60 compounds, whereby a C60 molecule is ionized 3− to C60 . In fact these compounds exhibit superconductivity Isolation of M@C60 (M: alkaline earth and lanthanide 6− between 18 and 30 K. In C60 , the LUMO is fully occupied metal) has been limited due to difficulties in purification and with six electrons and hence this material is insulating. the instability of the endohedral complexes. Other endohedral Metallic conductivity has been observed for C60 when C60 and C70 systems, such as Kr@C60 [67] and Dy@C60 [68] doped within a very narrow stoichiometry range. It turns out have been isolated. In these structures the ␲-orbital system that metallic endohedral C60 is difficult to produce. This fail- is perturbed. In particular, the Raman spectrum of Dy@C60 ure is attributed to the hybridization of metal ‘d’ orbitals with shows that three electrons are transferred from the Dy atom the carbon orbitals resulting in a donor–acceptor type bond- to the C60 cage, which is very different from N@C60 dis- ing [64]. cussed previously. In the following sections we first consider two examples, Kr@C60 that has been successfully isolated, 3.2. Endohedral C60 and C70 and LiC60 that exists as interstitial, exohedral Li and C60 and Li@C60 [69]. This is followed by a few examples of C60 A characteristic feature of endohedral fullerenes such as encapsulating rare-earth metal atoms. N@C60, P@C60, and N@C70 is that the enclosed atoms keep their ground state configurations and are localized in the 3.2.1. Kr@C60 center of the fullerenes. The atoms are freely suspended in Yamamoto et al. [67] isolated 140 ␮g of 90% pure the fullerene cages and exhibit properties resembling those Kr@C60 from a mixture containing 99.9% empty C60 and of ions in electromagnetic traps [65]. A special feature of measured its 13C NMR, IR and UV–vis spectra. The 13C N@C60 is that it gives a clear hyperfine split electron param- NMR spectrum of a mixture of 40% C60 and 60% Kr@C60 agnetic resonance (EPR) signal even in the solid state [66]. exhibits two signals at 143.23 and 143.62 ppm, respectively. This makes it an ideal probe for monitoring chemical reac- Thus, encapsulation of a Kr atom in the C60 cage causes no tions of C60 via changes in the EPR signal. Multiple func- perturbation of the Ih symmetry on the NMR time scale al- tionalization of the cages of N@C60 and N@C70 are possible though a downfield shift of 0.39 ppm is observed. without destroying the endohedral system. A second possible Fig. 5 compares the IR spectra of C60 and [email protected] use of N@C60 is in quantum computing [65] mainly due to former, the four IR-active (F1u) bands mentioned previously the long spin lifetimes and the fact the system can be con- are marked by A, B, C and D. The extra band at 1500 cm−1 trolled at ambient conditions. is due to the solvent CS2, which remained in the sample film S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1119 after solvent evaporation. Bands A, C and D of Kr@C60 are readily identifiable. The shoulder bands on the low-frequency side are due to empty C60 (10%). Band B is unexpectedly weak although the reason for it is not clear. Other bands were attributed to unidentifiable impurities. It was noted that Bands A, C and D were shifted to higher frequencies by 15.4, 10.6 and 8.2 cm−1, respectively, upon encapsulation of a Kr atom. In addition to the normal modes of the carbon cage, Kr@C60 is expected to show three IR-active (F1u) vibrations corresponding to three degrees of freedom of the encapsulated Kr atom. However, their frequencies are estimated to be near 100 cm−1 which was far below the measurable range. Fig. 6 compares the UV–vis spectra [67] of C60 and Kr@C60. In the 640–580 nm region, all four bands, ␥0, ␥1, ␥2 and ␥3 are red-shifted upon encapsulation of the Kr atom. These bands have been assigned to the components of a 1 1 symmetry-forbidden T1g ← A1g transition. Note that the A1g level lies deep down in the valence band, not shown in Fig. 4. γ0 and γ2 are the false origins separated from γ1 and γ3, respectively, by one quantum of the lowest Hg vibration −1 which was estimated to be 254 or 257 cm for Kr@C60. Thus, incorporation of a Kr atom does not change or slightly Fig. 6. Ground-state absorbance spectra of Kr@C60 and C60 dissolved in increases the vibrational frequency of this Hg mode. The methylcyclohexane/isopentane glasses at 77 K. Adapted from Ref. [67]. bands in the 420–370 nm region have been assigned to the 1 1 allowed 1 T1u ← A1g transition with A0 as the origin, and ration of the Kr atom into the C60 cage does not lower the encapsulation of a Kr atom slightly increased its frequency symmetry although it slightly perturbs the ␲-orbital system. − by 10–15 cm 1. This change is smaller and in the opposite This result is expected since no charge-transfer occurs from direction compared to the former symmetry-forbidden sys- the Kr atom to the cage. tem. The separations of A1,A2 and A3 from the origin were previously assigned to single quanta of the lowest frequency 3.2.2. Li@C60 1 Hg(1), Ag(1) and Hg(5) modes, respectively, in the 1 T1u Jantoljak et al. [69] carried out a vibrational study on state. Thus, Yamamoto et al. [67] determined these frequen- lithium-implanted fullerene films (LiC60), which include −1 cies to be 249, 429 and 1040 cm , respectively. Thus en- 25% endohedral Li@C60 as well as interstitial, exohedral 1 capsulation reduces these frequencies by ∼1% in the 1 T1u Li and C60 matrix. Fig. 7 compares the Raman spectra of electronic state. All the above results suggest that incorpo- LiC60 and pristine C60. In general, the bands observed for

Fig. 7. Comparison of the Raman spectrum of a pure and a lithium-implanted C60 ﬁlm at 20 K with the 514.5 nm line as the excitation line. The inset shows additional vibrational–rotational band from the two compounds. Reproduced from Ref. [69] with permission. 1120 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

−1 Fig. 8. Infrared absorption spectrum of LiC60 and C60. Additional absorption is seen in LiC60 between 350 and 600 cm region. Reproduced from Ref. [69] with permission.

LiC60 are broadened and some are shifted to lower frequen- fullerenes, Er@C60 may be slightly stabilized by forming a cies relative to those of C60. The pentagonal pinching (Ag(2)) weak charge-transfer complex with aniline. −1 −1 frequency near 1470 cm is known to be shifted by ∼7cm Inoue et al. [71] isolated Eu@C60 and observed the on- to a lower frequency per one electron transfer. In the present set of the absorption red shifted (>900 nm) in comparison −1 case, this band shifts from 1468.5 to 1464.2 cm , indicating with those of C60 and C70. The valence state of the Eu atom one electron transfer on average in every second C60 cage. was determined to be 2+ by Eu LIII-edge X-ray absorption The background in the 600–250 cm−1 region (shaded area near-edge spectroscopy (XANES). Basically XANES is a of the inset) was attributed to the vibrational–rotational tran- type of X-ray absorption fine-structure spectroscopy (XAFS) sitions predicted theoretically. The same background is also which uses the technique of modulating the X-ray absorption observed in the IR spectrum shown in Fig. 8. It is seen that coefficients at energies near and above an X-ray absorption the intensities of the F1u(1) and F1u(2) modes are reduced ap- edge. Typically XANES is a region of the X-ray absorption proximately by a factor of 1/3, although their frequencies and spectrum within ∼50 eV of the absorption edge. The oscil- widths are almost unchanged. This is contrast to intercalated latory structure in the X-ray absorption coefficient turns out fullerenes such as (K,Rb)xC60 in the metallic state where the to be a unique signature of a given material yielding infor- F1u(2) mode becomes much stronger than the F1u(1) mode mation on the local atomic coordination, chemical/oxidation and the latter is shifted significantly to a lower frequency states with minimum sample requirements. For a review on as x increases. Furthermore, the F1u(3) mode disappears and the XAFS/XANES see Ref. [72]. the F1u(4) mode is broadened considerably without changes The first report of an endohedral C60 with metallic proper- in frequency. These differences in IR spectra between LiC60 ties was on La@C60. Klingeler et al. [73] deposited individual and (K,Rb)xC60 support the interpretation that the former clusters of La@C60 onto graphite and used scanning tunnel- contains endohedral Li@C60. It was not possible, however, ing spectroscopy (STS) to probe the local density of states. to separate the contributions of the interstitial and exohe- STS determines the local electronic structure of a sample’s dral species from that of the endohedral fullerene in these surface and encompasses various methods. One of the meth- spectra. ods is to use a scanning tunneling microscope in order to collect current versus voltage (I–V) curves at every point in a 3.2.3. M@C60 (M: rare-earth metal) data set, providing a three-dimensional map of the electronic Isolation of M@C60, where M refers to a rare-earth metal structure. With a lock-in amplifier, dI/dV (conductivity) ver- atom, has been difficult since it is unstable in air and sol- sus voltage curves can be collected directly. Fig. 9 shows the uble in solvents that are not suitable for high-performance normalized differential tunneling conductivity as a function liquid chromatographic (HPLC). Er@C60 was first purified of the bias voltage for La@C60. A metal-like density of states by Ogawa et al. [70] via a combined technique of vacuum (zero band-gap) at the Fermi level (zero voltage) in La@C60 is sublimation followed by HPLC separation. A UV–vis and revealed. This can be interpreted in terms of charge donation ␲ near-IR absorption spectrum of Er@C60 in aniline shows a from the La atom to the C60 derived orbitals. The C60- characteristic peak at 500 nm with an onset at 1200 nm, which derived LUMO is expected to split in La@C60 due to charge is far in the red compared to that of C60 in aniline. Since the transfer and symmetry reduction. La@C60 becomes metal- metallofullerenes are better electron acceptors than the empty lic since t1u-derived orbital is partially filled upon charge S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1121

Fig. 9. The normalized differential tunneling conductivity (dI/dV)(V/I)asa function of the negative and positive bias voltages of La@C60 on graphite at room temperature. Adapted from Ref. [73].

Fig. 10. UV–vis–NIR absorption spectrum of isolated Ca@C72 in CS2 so- transfer. Moreover, the tunneling current of La@C60 at room lution. The insert shows a LD–TOF mass spectrum of the isolated Ca@C72. temperature increases linearly with the bias voltage, which Reproduced from Ref. [77] with permission. changes at lower temperatures; the cluster shows a reversible ∼ opening of a band-gap at a transition temperature of 28 K. 4. C72 and C74 The metal-like density of states in La@C60 results due to a charge donation from the trivalent La atom into C60 4.1. Ca@C72 and Ca@C74 3+ 3− derived ␲ orbitals (La @C60 ), as shown in Fig. 4. Ow- ing to the non-centrosymmetrical position of the La atom Thus far, empty C72 and C74 cages have not been isolated inside the C60 cage and charge donation, the icosahedral even in microscopic quantities although their IPR structures symmetry of C60 is lowered. This results in splitting of the are expected to be of D6d and D3h symmetries, respectively. C60-derived LUMO level and the t1u level is only partially However, Wan et al. [77] were able to obtain samples of pure ␤ ﬁlled as shown in Fig. 9. Consequently, the peaks below ( ) Ca@C72 and Ca@C74 enough to measure their UV–vis spec- ␤ and above ( ) the Fermi energy can be assigned to the t1u- tra in CS2 solution. As shown in Fig. 10, Ca@C72 exhibits the derived orbitals. The Fermi level is located within this split- spectrum with the onset of absorption near 1500 nm followed orbital unlike C60, where the Fermi level lies between the by several peaks in the 1200–1400 nm region. Such low en- hu and the t1u levels. The metallic properties of La@C60 ergy peaks in the absorption spectrum cannot be attributed to opens up the possibility of superconductivity and ferro- energy gaps between the valence band (HOMO) and the con- magnetism of endohedral fullerenes doped with rare-earth duction band (LUMO). The origin of these transitions is most atoms. probably from the LUMO to LUMO + nth level. These fea- Endohedral fullerenes of carbon cage size in the range be- tures are characteristic of the metal → cage electron-transfer. tween C66 and C84 are shown to be stable structures although Successful isolation of these endohedral fullerenes suggests the corresponding empty fullerenes are either not stable or that an unstable carbon cage can be stabilized by metal to cage have been isolated only in minor quantities in the fullerene charge-transfer. Fig. 11 illustrates two geometry-optimized soot. Amongst these, many of them do not follow the IPR structures of Ca@C74 based on ab initio calculations obtained rule. There are several ways in which the IPR can be vio- by these workers. In their method the geometry optimization lated; one way is to generate fused-pentagons in which the was done at the HF level with a 3-21G basis set for the carbon pentagons are adjacent to one another. Isolation and struc- atoms (see Section 2.2). In Fig. 11, (a) is more stable than ture determination of Sc2@C66 [74] and Sc3N@C68 [75] (b), and the Ca atom is along the symmetry axis but not at the from NMR spectra clearly show that these carbon cages have center of symmetry. As a result, the overall symmetry is re- non-IPR structures. The Sc2@C66 X-ray structure is of space duced from D3h to C2v. Ab initio calculations by Kobayashi group Pmn2 and the structure contains two pairs of two-fold fused pentagons with closely situated two Sc atoms [74]. The yield and stability of fullerenes with carbon cages in the size group C70 and C84 strongly depend upon the enclosed metal. Dunsch et al. [76] have isolated various metallofullerenes such as La2@C72,Ce2@C72, Eu@C74, Tm@C78, and [email protected]@C72 and Ce2@C72 show similar features in their absorption. The stability of Tm@C78 is much lower than Eu@C74. In the following sections we discuss only a limited number of endohedral fullerenes and mainly focus Fig. 11. Optimized structures of Ca@C74 ab initio calculation. Structure (a) is 7 kcal/mol more stable than structure (b). Since the calcium atom is not on those where the UV–vis and vibrational spectra have been in the center, the symmetry of both structures decreases from D3h to C2V. measured. Reproduced from Ref. [77] with permission. 1122 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

Fig. 12. vis–NIR spectrum of Eu@C74 in CS2 solution. Reproduced from Ref. [80] with permission. and Nagase [78] and Akasaka and coworkers [79] have been one heptagon surrounded by five adjacent pentagons. These carried out using Gaussian 94 (previous version of Gaussian predictions were partly confirmed by later experimental work 03 [16]) at the Hartree–Fock level with subsequent improve- [74,75]. ments using the BLYP energy levels and the 6-31G basis set (see Section 2.2). These calculations suggest that more stable 4.2. Eu@C74 structures may be obtained if one considers non-IPR structures. For example, they suggested one structure containing Kuran et al. [80] isolated the first europium endohedral a pair of adjacent pentagons and another structure containing fullerene, Eu@C74, and measured its vis–NIR, IR, Raman and ESR spectra. As seen in Fig. 12, it exhibits eight absorption maxima in the 500–2500 nm region (CS2 solution). All these bands were assigned to the ␲ → ␲* transitions of the carbon cage because they blue-shift upon changing the solvent to toluene which is less polar. Fig. 13 shows the IR and Raman spectra obtained in the solid state. Both spectra exhibit approximately 50 bands in the 1600–200 cm−1 region where the carbon cage vibrations appear. These numbers are more than those expected from the strict selection rules of D3h point group. Thus, the symmetry of Eu@C74 must be −1 lower than D3h. The Raman band at 123 cm was assigned to the Eu C74 cage vibration based on vibrational frequencies known for other endohedral metallofullerenes.

5. C78

The C78 cage consists of 12 pentagons and 29 hexagons which lead to five IPR structures of D3,C2v(a), C2v(b), D3h(a), and D3h(b). Thus far, three stable isomers have been isolated, and their symmetries (C2v(a), C2v(b), D3h) have been confirmed by 13C NMR spectroscopy [81]. Sc3N@C78 is more abundant than any of the other con- ventional metallofullerenes such as Sc2@C84. Olmstead et al. [82] have isolated Sc3N@C78, characterized it by UV–vis spectroscopy, and carried out X-ray analy- Fig. 13. IR and Raman spectrum of solid Eu@C74. Reproduced from Ref. [80] with permission. sis on [Sc3N@C78]Co(OEP)1.5C6H60.3CHCl3(OEP: oc- S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1123 taethylporphyrin). The UV–vis absorption spectrum of air- stable Sc3N@C78 in CS2 shows peaks at 460, 623 nm with shoulders at longer wavelengths. These workers proposed an overall D3h symmetry. Recently Campanera et al. [83] have carried out DFT calculation of Sc3N@C78 (theoretical mech- anism is described in Section 6.2). They find that the metal ions are strongly linked to three [6:6] junctions of three different pyracylene patches located at the midsection of the fullerene cage. Thus, the Sc3N moiety is strongly bonded to the cage preventing any free rotation. This is in contrast to their theoretical calculation of Sc3N@C80 (as discussed in Fig. 14. (A) Optimized D2h structure of La2@C80. (B) Circular motion of Section 6.2) where the Sc3N shows a free rotation within the the two La atoms inside the Ih cage of C80. Reproduced from Ref. [88] with C80 cage. permission.

13 13 6. C80 due to the C C coupling. This was attributed to a near- spherical cage resulting from circular motion of two La atoms The C80 cage consists of twelve pentagons and thirty inside the carbon cage as illustrated in Fig. 14B. The observed hexagons. There are seven IPR-satisfying structures (D2,D5d, small line width suggests that the two signals expected for C2v(a), C2v(b), D3,D5h and Ih) for the C80 cage [84,85]. The Ih symmetry are too close to be observed as separate signals. Ih isomer is most unstable; however, it becomes stable upon Since there is a small barrier for such a motion, it should be charge transfer. In this symmetry, there are two types of car- possible to stop the La atoms at the most stable positions by 13 bon atoms, 20 atoms with C3v site symmetry and 60 atoms lowering the temperature. In fact, they observed a broad C with C5 site symmetry. Encapsulation of the two La atoms NMR signal at 258 K which was attributed to an overlap of the inside the Ih symmetry is most favored as discussed in the 13 signals expected for D2h symmetry. They also observed next section. a single 139La NMR signal at 258 K which is broadened by raising the temperature from 305 to 363 K. 6.1. La2@C80 Fig. 15 shows the IR spectrum of La2@C80 in the range from 353 to 83 K obtained by Moriyama et al. [89]. Under Theoretical studies (using Gaussian/DFT) by Kobayashi Ih symmetry, the 234 (3 × 80 − 6) normal vibrations of its 6− et al. [85] show that the empty C80 cage is most stable when C80 cage are grouped into the following symmetry species: it takes the D2 or D5 structure, and the D2 structure has been 3Ag +Au +4F1g +6F1u +5F2g +7F2u +8Gg +8Gu + 11Hg + 13 conﬁrmed later by C NMR spectrum which exhibits 20 9Hu. However, only 14 (3Ag + 11Hg) are Raman-active, and signals [86]. Their calculations also show that the carbon only 6 (6F1u) are IR-active. Their IR spectrum shows one −1 cage of endohedral La2@C80 takes Ih symmetry as a re- strong band at 1384 cm and four weak bands at 1463, sult of charge-transfer from the La atoms to the carbon cage 1232, 680 and 505 cm−1 which are evident at 83 K. This 3+ 6− ((La )2(C80) ) [87]. This Ih structure is stabilized because spectral pattern is in fairly good agreement with the results 6− the four-fold degenerate HOMO occupied by two electrons of their theoretical calculations on the C80 cage of Ih can accommodate six more electrons to form the closed shell symmetry. The line width of the 1384 cm−1 band decreases structure with a large HOMO–LUMO gap. There are no distinct minima in the electrostatic potential indicating that the encapsulated metals can freely rotate inside the C80 cage. Furthermore, these workers proposed the overall D2h structure shown in Fig. 14A in which the two La atoms (ca. 3.66 A˚ apart) are located on a C2 axis passing through the centers of two hexagons and each La atom is ca. 2.6 A˚ from the hexagonal carbon atom. Akasaka et al. [88] carried out 13C as well as 139La NMR studies of La2@C80 to conﬁrm their theoretical predictions. The 139La NMR spectrum measured at 296 K exhibits a single signal at −402.6 ppm with a line width of 113 Hz, suggesting that the two La atoms are equivalent inside the cage. As discussed later, two signals are expected for the C80 cage of Ih symmetry. However, the 13C NMR spectrum of 13C-enriched sample (25% 13C) of La @C at 300 K exhibits only one sig- 2 80 Fig. 15. Infrared spectra of La2@C80 in KBr pellet at temperatures between nal at 141.61 ppm (line width, 0.08 ppm) with satellite bands 83 and 353 K. Reproduced from Ref. [89] with permission. 1124 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

II Fig. 17. Crystal structure of [Sc3N@C80]Co (OEP)1.5CHCl30.5C6H6 perpendicular to the mirror plane that bisects Co, Sc1, and N. Reproduced from Ref. [91] with permission.

6.2. Sc3N@C80

Stevenson et al. [91] first prepared a new family of stable endohedral metallofullerenes, A3−nBnN@C80 (n = 0–3, A, B = rare-earth metal) that are stabilized by donation of up to six electrons to the C80 cage. The introduction of N2 during the growth process results in the isolation of a few mil- Fig. 16. Mode displacement pattern of the three nondegenerate modes in Ih ligrams of the sample. Members of this class are formed by 6− ν ν C80 : (a) breathing mode Ag( 1), (b) out-of-phase radial mode Ag( 2) and a trimetallic nitride template (TNT) process, which ensures (c) pentagonal-pinch mode Ag(ν3). The experimental values of the nonde- endohedral formation in the electric-arc process. Sc3N@C80 generate frequencies of C60 are shown. belongs to this family, where the charge redistribution re- 6+ 6− sults in (Sc3N) (C80) . These workers isolated 2–4 mg of Sc3N@C80 from ∼60 mg of the product, determined the crys- monotonically upon lowering the temperature from 353 K tal structure, and measured the UV–vis and 13C NMR spectra −1 −1 (14 cm ) to 83 K (1.5 cm ). However, the number of of Sc3N@C80. The results confirmed that the Sc3N moiety is observed bands does not reflect the effect of lowering the encapsulated in the C80 cage of Ih symmetry which is stabi- symmetry from Ih to D2h at low temperatures. According lized by the charge-transfer between them. These endohedral to theoretical calculations on La2@C80 of D2h symmetry, fullerenes are the first examples containing relatively large the La La vibrations in the two directions perpendicular to molecules inside the carbon cage. Since the trimetallic ni- −1 the La La axis are at 72 and 66 cm . It was not possible, trides such as Sc3N and ErSc2N are stable only in the endo- however, to observe these low-frequency modes at low hedral state, the preparative method developed by Stevenson temperature. et al. has opened a new field of synthetic inorganic chemistry. Distinction of Ih and D2h symmetries of the C80 cage may Fig. 17 shows the crystal structure of [Sc3N@C80] II be made more easily if one measures the polarized Raman Co (OEP) 1.5CHCl30.5C6H6. It is seen that the trigonal spectra of La2@C80. This is because the number of totally planar Sc3N moiety is encapsulated inside the C80 cage II symmetric (Ag) vibrations should be only three for the Ih and is close to Co (OEP) which makes face-to-face con- II structure while that of the D2h structure is much larger. Thus, tact with another Co (OEP). The Sc N distances (2.011 the number of polarized bands should increase markedly and 1.966 A)˚ are slightly shorter than the Sc N bonds in as the temperature is lowered (Ih → D2h). Fig. 16 shows [(HSiMe2)2N]3Sc(THF)(average distance, 2.069 A).˚ In the schematic of the normal mode displacement pattern of the solid state, the Sc atoms face three pentagons inside the C80 three totally symmetric vibrations of the C80 cage of Ih sym- cage. Later, X-ray analysis was carried out on a mixed metal metry [90]. The calculations were performed for a charged analog ErSc2N@C80 [92]. 6− C80 molecule (without any metal cluster in the cage) using The UV–vis spectrum of Sc3N@C80 shows prominent first-principles quantum molecular dynamics method in the peaks at 900 and 1140 nm and strong absorption below LDA approach [39]. The corresponding frequencies observed 1000 nm. The band-gap energy corresponds to the absorp- for the Ih C60 are also listed. The radial breathing and pen- tion onset (∼1560 nm) [91]. It is only 0.8 eV, which is much tagonal pinching modes are essentially similar for both cages. smaller than that of the 1.3 eV band-gap in La2@C80. However, the “uneven breathing mode” is unusual and unique The C80 cage of Ih symmetry consists of two types of to the C80 cage. It is a totally symmetric mode in which the carbon atoms; 60 atoms are located at the vertices where two 60 pentagon atoms move out of phase from the remaining 20 hexagons and one pentagon meet (corannulene-type), and the atoms. remaining 20 atoms are located at the vertices where three S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1125 hexagons meet (pyrene-type). Thus, the 13C NMR spectrum of Sc3N@C80 exhibits two signals at 144.57(corranulene- type) and 137.24 ppm (pyrene-type) in 3:1 intensity ratio. This result suggests that dynamic motion of the Sc3N moiety inside the cage yields a time-averaged electronic environment of Ih symmetry, and that the Sc3N cluster is not located at any specific bonding site at least on the NMR time scale at 295 K [91]. Further support of this dynamic behavior is given by the 45 observation that Sc3N@C80 exhibits a single signal in Sc NMR spectrum. It is interesting to note that the 13C NMR spectrum of La2@C80 exhibits only one signal in spite of the Ih symmetry of its C80 cage due to the reason discussed previously [89]. Krause et al. [93] investigated the IR and Raman spectra of Sc3N@C80 to determine the nature of the C80 Sc3N interaction. As mentioned earlier, the C80 cage of Ih symmetry exhibits 6 IR and 14 Raman fundamentals. The trigonal- Fig. 19. Low energy infrared and Raman spectrum of Sc3N@C80 and Y3N@C80 at 300 K. Adapted from Ref. [93]. planar Sc3N moiety of D3h symmetry exhibits three IR and three Raman fundamentals. If there is no interaction between them, one should expect 9 IR and 17 Raman fundamentals. two times larger than that of Sc (44.96). It was attributed to However, these workers observed 69 bands (10 IR, 32 Raman the particular bonding properties of the encaged Y3N moi- and 27 IR/Raman) excluding very weak bands. Violation of ety although the origin of this unusual observation is not the mutual exclusion rule indicates that the Ih symmetry is clear. lowered significantly as a result of the Sc3N C80 interaction. Theoretical calculations of Sc3N@C80 by various groups Fig. 18 shows the IR and Raman spectra obtained at 300 K. predict different structures. Recently Campanera et al. [83] It is seen that the Raman spectra obtained by 647 and 514 nm used DFT to examine the bonding between Sc atoms and the excitations are resonance-enhanced because these lines are fullerene cage in Sc3N@C80. Their calculations were car- close to the electronic transitions at 2.0 and 2.5 eV, respec- ried out with the ADF set of programs [28]. They used the tively. local spin density approximation together within the LDA The vibrations due to the Sc3N moiety (D3h symmetry) approach [20]. TZ + polarization Slater basis sets (see Sec- were identified by comparing the IR and Raman spectra tion 2.2) were employed to describe the valence electrons −1 of Sc3N@C80 and Y3N@C80. In the 800–200 cm region, of C and N. For Sc3N@C80, the energy difference between − only three Raman bands at 599, 411 and 210 cm 1 are metal- isomers of different Sc3N orientations in the carbon cage sensitive, and shifted to 709, 429 and 194 cm−1, respectively, is rather small (less than 2 kcal/mol). They find that the by Sc/Y substitution (Fig. 19). These bands were assigned to Cs symmetry where the three metal ions are oriented to- the antisymmetric stretching (E , IR/R), symmetric stretch- ward [6:5] ring junctions has the lowest energy, as shown in Fig. 20. The relative energies for the various isomers re- ing (A1, R) and in-plane bending (E , IR/R) vibrations of the planar Sc3N moiety, respectively. This result is somewhat sult in their conclusion that the Sc3N unit may easily rotate unexpected since the atomic weight of Y (88.91) is about inside the fullerene cage. This is in contrast to Sc3N@C78 where the Sc ions are strongly linked to the [6:6] ring junctions of pyracylene patches; this bonding restricts the Sc3N unit to freely rotate within the fullerene cage (vide supra) [83]. Kobayashi et al. [94] have used nonlocal density functional calculations at the BLYP level (a gradient- corrected functional) to calculate the electronic structure of Sc3−nLanN@C80 (n = 0–3). For n = 0, they find that the large positive charges on Sc are very effective for electrostatic interactions with the negatively charged N atom and the carbon cage. For the pyramidal Sc3N cluster, however, severe electrostatic repulsion is expected from the carbon cage. Because of this the Sc3N adopts a planar structure with long Sc Sc distances in Sc3N@C80. They find that there are two structures of Sc3N@C80 with Cs symmetry that are almost isoenergetic. These results suggest that the Sc N ion is not stabilized at Fig. 18. Infrared and Raman spectrum of Sc3N@C80 at 300 K. Adapted 3 from Ref. [93]. specific internal bonding sites but can rotate freely inside the 1126 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

Fig. 20. Relative energies (in eV), symmetries, and carbon chains with schematic position of Sc atoms in a 2D representation for the optimized isomers of Sc3N@C80. The 3D representation for isomers 6 (C2v) and 11 (Cs) shows the connections between the metal ions and carbons. Reproduced from Ref. [83] with permission. fullerene cage, thus stabilizing the Ih symmetry of the C80 The structure of Sc3N@C80 still remains somewhat of an cage. open question since various theoretical works predict differ- In contrast to the above two theoretical results, calcula- ent optimized structures. This makes it vital for additional tions by Krause et al. [93] show evidence of a chemical experimental evidence using Raman scattering and IR ab- bond between the Sc3N ion and the C80 cage which hin- sorption. Since Ih C80 has three Raman-active frequencies ders the rotation of the Sc3N cluster inside the fullerene of Ag symmetry, polarized Raman studies mentioned earlier cage. They used the DFT scheme employing a nonorthog- should reveal the actual structure of the endohedral fullerene onal tight-binding model [95] to determine the energy and on the vibrational time scale. forces for a given atomic conﬁguration. It turns out that their Other TNT endohedral fullerenes include La3N@C80. Ac- method is highly transferable and has been applied to de- cording to Kobayashi et al. [94] the La3N cluster main- termine the structures, total energies, and vibrational prop- tains a pyramidal structure and donates up to eight electrons 8+ 8− erties of carbon molecules, solids and clusters. Their opti- to the fullerene cage, forming (La3N) @C80 . The addi- mized structure is that of C3 symmetry since the Sc atom tional electrons occupy the four-fold degenerate LUMO of is not located exactly below the center of the pentagon and C80, resulting in an open shell electronic structure that has each Sc C distance is slightly different (±0.2 A).˚ Their DFT a high reactivity. Repulsion between the La atoms and the calculations also predict vibrational frequencies and IR inten- long La N bond lengths prevents planarization of the La3N sities of Sc3N@C80 which are in fairly good agreement with molecule inside the cage. This makes La3N@C80 less stable those observed. In addition to the internal vibrations of the than Sc3N@C80. C80 cage and the Sc3N moiety, four vibrations were predicted −1 under C3 symmetry in the region below 150 cm . These are the vibrations due to the translational and rotational motions 7. C82 of the Sc3N moiety in the C80 cage which are regarded as the Sc3N C80 vibrations. They were observed around 133, There are nine IPR-satisfying isomeric structures hav- −1 108, 78 and 48 cm for Sc3N@C80 and around 110, 96, ing C2(a), C2(b), C2(c), C2v,Cs(a), Cs(b), Cs(c), C3v(a) and −1 66 and 36 cm for Y3@C80. Although this result seems to C3v(b) symmetries are for the C82 cage [96]. Lebedkin et al. 13 contradict the C NMR study which suggests Ih symmetry, [97] studied the Raman, far-IR and inelastic neutron scat- Krause et al. [93] suggest that the isomerization between 20 tering (INS) spectra of M@C82 where M is La, Y, Ce and equivalent conﬁgurations can be time-averaged to produce Gd. Theoretical calculations show that La@C82 and Sc@C82 Ih symmetry on the NMR time scale. In contrast to Steven- have C2v symmetry [98]. In the latter metallofullerene, Sc son et al. [91], these workers [93] noted that a large band gap (3d14s2) atom prefers to donate two valence electrons to the (slightly over 2.0 eV) resulting from the charge-transfer leads C82 cage because of the low lying ‘d’ orbitals, whereas La to a close-shell structure which is responsible for its high donates all three valence electrons to the fullerene cage. In stability. Gd@C82, three valence electrons of Gd are transferred to the S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1127

Fig. 21. Electron transfer between Gd and C82 in Gd@C82. Adapted from Ref. [6]. Fig. 23. Dependence of the Raman frequency of the metal-to-cage vibration LUMO level of C . Each of the occupied orbitals of C has in M@C82 on the reduced mass of the endohedral metal atom. Adapted from 82 82 Ref. [97]. a very small tail on the 5d of Gd as a result of a slight back transfer. However, the UV–vis spectra reﬂect only the orbital and Gd compounds. If the metal–cage vibration is approxi- picture shown in Fig. 21. mated by a diatomic vibrator, its frequency, ν (cm−1), is given Fig. 22 shows the Raman spectra of monometallic endo- by hedral fullerenes obtained by Lebedkin et al. [97] The spectra above 200 cm−1 are very similar indicating a similar carbon f 1/2 ν = . , cage structure for all four compounds. One of the three struc- 4 12 µ (10) 13 tures having C2 symmetry is most probable according to C NMR and theoretical studies by other workers. In contrast, where f is the force constant (dyne/cm) and µ is the re- − the metal-sensitive bands are observed below 200 cm 1;at duced mass (atomic weight unit) of the M C82 molecule. 183, 163, 162 and 155 cm−1 respectively, for the Y, La, Ce Fig. 23 [97] shows a linear plot obtained between ν and µ−1/2 from which the average value of f was calculated to be 1.75 × 105 dyne/cm. These results indicate that the magni- tude of the M C82 interaction is similar among the four compounds and the M C82 bonding is essentially ionic, namely, 3+ 3− M C82 . The IR spectra above 200 cm−1 are also similar for the four compounds. However, the Y and La compounds exhibit very strong and broad bands near 54 and 50–45 cm−1, respectively. In contrast to the “longitudinal” metal–cage vibrations observed in the Raman spectra, these low-frequency IR bands were attributed to the “lateral” metal–cage vibrations. Krause et al. [99,100] measured the Raman and IR spectra of Tm@C82 and Gd@C82. The Raman spectra of the three isomers of Tm@C82 are clearly different in the high- frequency region but their metal–cage vibrations appear in the same region (117 cm−1 for isomers A and B and 116 cm−1 for isomer C). These values are signiﬁcantly lower than that ex- 3+ 3− pected from a linear plot obtained for a series of M C82 2+ 2− type compounds. Thus, the Tm C82 formulation was suggested to indicate a weaker ionic interaction. Xu et al. [101] isolated four isomers (I, II, III and IV) of Ca@C82 and obtained the UV–vis–NIR spectra shown in Fig. 24(a). Isomers II and III exhibit distinct absorption onsets at around 1000 and 1200 nm, respectively, whereas isomers I and IV show less distinct onsets at around 1800 nm. In general, these spectra exhibit much more distinctive structures than those containing group IIIA metals such as Sc, Fig. 22. Raman spectra of M@C metallofullerenes, M = La, Y, Ce, Gd. Y(Fig. 24(c)) and La. As stated earlier, the electronic 82 3+ 3− Adapted from Ref. [97]. state of M@C82 (M = Y and La) is expressed as M C82 . 1128 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

[103]. It was found that the overall symmetry is C3v and the Sc Sc distance is 2.3(3) A.˚ In this case, the charge-transfer 3+ 3− state is expressed as Sc3 @C82 . − Akasaka et al. [104] prepared the La@C82 anion which exhibits a unique stability toward air and water and determined its symmetry by 13C NMR spectroscopy. A-form exhibits 24 lines which are expected for C2v symmetry while B-form shows 38 lines conﬁrming its Cs symmetry. Recently Inoue et al. [105] isolated an endohedral fullerene, Y2@C84, which was found to be a metal carbide (Y2C2) encapsulated in the C82 cage, namely, (Y2C2)@C82. The electronic spectrum exhibits two bands at 684 and 880 nm with the onset of the absorption at 1100 nm. From the analysis of the 17 line 13C NMR spectrum, it was suggested that the Y2C2 moiety takes a diamond-shaped structure and rotates rapidly inside the spherical C82 C3v cage. Similar results are reported previously for (Sc2C2)@C84 discussed in the following section.

8. C84

The C84 cage can take 24 isomeric structures as shown by Manolopoulos and Fowler [84]. Inakuma et al. [106] isolated the three isomers (I, II and III) of Sc2@C84 and determined their structures by 13C NMR spectroscopy. As shown

Fig. 24. UV–vis–NIR absorption spectra of (a) Ca@C82(I–IV), (b) in Fig. 26, isomer I exhibits 38 lines of nearly equal intensity Ca@C82(I, II), and (c) Y@C82(I) for comparison. Reproduced from Ref. and eight additional lines of half intensity marked by aster- [101] with permission. isks. Isomer II exhibits 18 lines plus 6 lines of half intensity,

2+ 2− Thus, the M C82 formulation was suggested for Ca@C82. The exact position of the metal in the C82 cage cannot be determined by spectroscopic methods. Using synchrotron powder diffraction method, Nishibori et al. [102] were able to determine the cage symmetry of Sc@C82 (isomer I) to be C2v and locate the Sc atom at an off-center position on the C2 axis as shown in Fig. 25. The nearest Sc C distance obtained from the charge density map was 2.53(8) A˚ and the Sc C82 charge- transfer was estimated to be 2.2 e. This work was extended to Sc3@C82 which contains an equilateral triangular Sc cluster

Fig. 25. (A) C2v cage symmetry of Sc@C82 where the Sc atom is located 13 at an off-center position on the C2 axis. (B) Electron density distribution of Fig. 26. C NMR spectra of Sc2@C84(I, II, III) in CS2 at room temperature. Sc@C82 for the (1 0 0) section. Reproduced from Ref. [102] with permission. Reproduced from Ref. [106] with permission. S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132 1129

Fig. 28. Far-IR spectra of Sc2@C84(I, II, III) and C84 at room temperature. The metal–cage modes are indicated by arrows. Reproduced from Ref. [106] with permission.

around 100 cm−1 which consist of two bands (marked by arrows) and weak bands near 160–165 cm−1. The corresponding Raman spectra are shown in Fig. 29 [106] where the arrows indicate metal–cage vibrations. These metal–cage vi-

Fig. 27. Molecular structures for Sc2@C84(I, II, III). Reproduced from Ref. brations were assigned based on a linear three-mass oscilla- [106] with permission. tor model [106] shown in Fig. 30. In the case of isomer III of D2d symmetry [109] the Sc C84 cage modes were assigned at and isomer III exhibits 10 lines plus one line of half inten- ∼250 cm−1 (symmetric stretch), ∼170 cm−1 (antisymmetric −1 sity. Based on these observations, the symmetries of isomers stretch), and ∼125 cm (bending). The calculated Sc C84 I, II and III are definitively assigned to CS,C2v and D2d, stretching force constant was 1.19 dyne/cm which is close to respectively. The molecular structures consistent with these those of Tm@C82 (1.18 dyne/cm for isomer A). Since the 2+ 2− NMR data are shown in Fig. 27 [106]. The D2d structure of latter is known to be Tm C82 , the charge state of the Sc isomer III has been confirmed by synchrotron X-ray diffrac- atoms in Sc2@C84 was concluded to be near 2+. tion studies [107] and topological analysis of electron density Sc2C2@C84 is a highly stable compound, and Wang et distribution [108]. al. [110] were able to isolate 3.5 mg of the sample to carry The UV–vis–NIR spectra of the three isomers are clearly out UV–vis, 13C NMR and synchrotron X-ray diffraction different from each other. Isomer I shows absorption maxima studies. The UV–vis spectrum exhibits an absorption onset (or shoulders) at 1204, 1045, 862, 730 and 660 nm, whereas at 1410 nm and a strong absorption at ca. 600 nm. This is isomer II exhibits broad absorptions at around 1770, 1425 markedly different from those of Sc2@C84(I, II and III) [106]. and 1000 nm. In contrast, isomer III shows no absorption The 13C NMR spectrum shown in Fig. 31 consists of 11 sig- in the 1300–2000 nm region. The red-shift of the absorption nals similar to that of Sc2@C84(III) of D2d symmetry plus onset of isomer II relative to I and III accounts for the much one extra signal at 91.99 ppm (signal 12). The former 11 sig- lower production efficiency and stability of isomer II relative nals are due to the carbon atoms of the cage whereas the to isomers I and III. latter originates in the sp-hybridized carbide carbon atom. The far-IR spectra of the three isomers of Sc2@C84 and The molecular structure determined by synchrotron X-ray the empty C84 cage (D2d symmetry) are compared in Fig. 28 powder diffraction studies show that the Sc2C2 moiety takes [106]. The metal–cage vibrations appear as the broad bands a diamond-shaped structure with the Sc Sc and C C dis- 1130 S. Guha, K. Nakamoto / Coordination Chemistry Reviews 249 (2005) 1111–1132

tances being 4.29 and 1.42 A,˚ respectively. The Sc C distance (2.26 A)˚ is close to that of ScC2 (2.135 A)˚ which was theoretically predicted. The compound is formulated as 2+ 2− (Sc2C2) @C84 since the charge density distribution studies show that the Sc2C2 moiety is in the 2+ state.

9. Summary and prospect

This review describes the current status of structural and spectroscopic studies on endohedral fullerenes. These studies have shed light on the structure of the carbon cage, the location and the structure of the encapsulated species inside the cage and the nature of interaction between them. Endohedral fullerenes are highly important not only for their unique structures but also for their potential to become superconducting materials. Thus far, endohedral fullerene research has been hindered by the limited availability of the sample (typically in the mg–␮g range). This situation will drastically change once preparative techniques are improved and a variety of species are encapsulated inside the carbon cage. Encapsula- tion is a novel synthetic method to prepare chemical species which are highly unstable “outside the carbon cage”. Many small inorganic species thus far unknown may be prepared by using the current and improved techniques. Fig. 29. Raman spectra of Sc2@C84(I, II, III) and C84 at room temperature. The metal–cage modes are indicated by arrows. Reproduced from Ref. [106] with permission. Acknowledgements

We would like to thank Dr. Gary Adams of Arizona State University for the pictorial representation of the totally symmetric vibrations in Ih C80 and other useful discussions. One of us (SG) thanks Jose´ Menendez´ and John B. Page for invalu- able insights in the ﬁeld of light scattering from fullerenes. We thank Carsten Ullrich for valuable comments on the theoretical methodologies.

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